$SO(N{)}_2$ Braid group representations are Gaussian

Abstract

We give a description of the centralizer algebras for tensor powers of spin objects in the pre-modular categories $SO(N{)}_2$ (for $N$ odd) and $O(N{)}_2$ (for $N$ even) in terms of quantum $(n-1)$-tori, via non-standard deformations of $U{\mathfrak{so}}_N$. As a consequence we show that the corresponding braid group representations are Gaussian representations, the images of which are finite groups. This verifies special cases of a conjecture that braid group representations coming from weakly integral braided fusion categories have finite image.

Typos fixed, exposition improved, proofs and statements of Corollary 2.4 and Theorem 4.6 expanded. version 3--two typos corrected. Version 4--close to published version, typos corrected

References in corpus (2)

• The N-eigenvalue Problem and Two Applications
• Braid representations from quantum groups of exceptional Lie type

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